Heretofore, there have been proposed various types of rich-lean combustion burners (for example, see Patent Literature Publications 1, 2 and 3). In such a rich-lean combustion burner, a lean-side mixture whose air ratio (the ratio of the amount of air to the amount of fuel) is in excess of 1.0 is burned at lean-side flame holes for the accomplishment of NOx reduction while for the stabilization of combustion flames, rich-side flame holes where a rich-side mixture whose air ratio falls below 1.0 is burned are arranged adjacent to the lean-side flame holes.